Is Death of a Salesman a Greek tragedy according to Aristotle?

Death of a Salesman is not a Greek Tragedy, according to Aristotle.

Basically, a Greek tragedy is about a prosperous, renowned character bringing about his own downfall through a fatal flaw. Willy Loman is not prosperous or renowned, and you could argue whether he has a fatal flaw or suffers from clinical depression. 

In Poetics, which you can , Aristotle said that a proper tragedy must have six elements: Plot, Characters, Diction, Thought, Spectacle, and Melody, and then he went on to define details of these six elements.

Plot: Aristotle said that the plot should at least have a "change of fortune," or catastrophe. Fortune refers to fate. Willy Loman's fortune doesn't change in the plot of Death of a Salesman. At the beginning he is poor and depressed, and at the end he is poor and depressed (and dead.)

Characters: According to Aristotle, the main character should be renowned and prosperous, so his reversal of fortune can be from good to bad, and the change should come about from a frailty in character, or character flaw. Willy Loman, though he wishes to be "well-liked," is not, as evidenced by the poor turn-out at his funeral. He certainly isn't prosperous.

Aristotle doesn't explain much about the third element, Thought, but Death of a Salesman seems thoughtful enough.

However, in the fourth element, Diction, Aristotle expects a 'good command of metaphor.' There are several excellent metaphors at work in Death of a Salesman, such as stockings symbolizing Willy's guilt over his extramarital affair.

Next is Melody. Aristotle's Greek tragedy should have a fully-integrated Chorus. Death of a Salesman has no chorus.

Aristotle also mentions Spectacle, but he prefers for a play to not rely too heavily on spectacle. When you read the stage directions, you can see that Miller uses a lot of lighting and other effects to enhance dream sequences and create a mood of pity and terror.

Finally, the tragedy should end in catharsis, or the purging of emotion. This catharsis should leave the audience with a feeling of pleasure. While sad and pathetic, Death of a Salesman has never left me personally with a catharsis or a feeling of pleasure. You may have a different response.

Overall, however, Death of a Salesman does not fit the definition of a Greek tragedy according to Aristotle.